Practice Solving Differential Equations Using Fourier Transform (11.9) - Fourier Transform and Properties
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Solving Differential Equations Using Fourier Transform

Practice - Solving Differential Equations Using Fourier Transform

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Practice Questions

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Question 1 Easy

What is the Fourier Transform used for in solving ODEs?

💡 Hint: Consider how transforms change the perspective on the equations.

Question 2 Easy

Name the main benefit of using the Fourier Transform for differential equations.

💡 Hint: Think about the complexity of dealing with derivatives.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the primary advantage of using Fourier Transform to solve ODEs?

It eliminates the need for initial conditions.
It converts differential equations into algebraic equations.
It simplifies the equations with non-linear terms.

💡 Hint: Think about how complex the derivatives make the equation before transformation.

Question 2

True or False: The Inverse Fourier Transform is used to convert frequency domain data back to the time domain.

True
False

💡 Hint: Recall the purpose of the Inverse Transform.

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Challenge Problems

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Challenge 1 Hard

Solve the differential equation d²y/dt² - 4y = sin(t) using the Fourier Transform method.

💡 Hint: Pay attention to how sine functions convert in the frequency domain.

Challenge 2 Hard

Consider the ODE d²y/dt² + 5dy/dt + 6y = e^(-t) for t > 0. Use Fourier Transform methods to find y(t) for t > 0.

💡 Hint: Remember to handle the exponential function carefully when transforming.

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